Heat the oven to 325°F. Snip off the stem of each fig and cut each into quarters, lengthwise; put the figs in a medium bowl, cover with hot water, and soak for 20 minutes.
Meanwhile, butter the bottom of a 13 x 9-inch baking pan and line with waxed paper. Butter the paper and the sides of the pan. In a small bowl, combine the flour, baking powder, baking soda, and salt. With an electric mixer, beat the peanut butter, brown sugar, 1/2 cup of the granulated sugar, and the butter until light and fluffy. Beat in the egg and water; scrape down the sides of the bowl. Beat until the mixture looks creamy. Beat in the flour mixture just until combined.
Drain the figs well and toss them with the remaining 2 Tbs. sugar and the cinnamon. Arrange the figs, cut side down, in one layer in the lined pan. Sprinkle the granola on top, filling the spaces between the figs.
Drop spoonfuls of the dough on top of the figs and then spread it evenly in the pan. Bake in the middle of the oven until the edges are very lightly browned, 35 to 40 minutes. The edges will be slightly puffed; press them down with a spatula to flatten. Let cool until the pan is warm to the touch. Invert the pan onto a cutting board, remove the pan and peel off the paper. (If any figs pull away, simply replace them.) Let cool completely before slicing into 18 bars (or into smaller pieces, if you like).